1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Aloiza [94]
2 years ago
15

A room has eight switches, each of which controls a different light. Initially, exactly five of the lights are on. Three people

enter the room, one after the other. Each person independently flips one switch at random and then exits the room. What is the probability that after the third person has exited the room, exactly six of the lights are on? Express your answer as a common fraction.
Mathematics
1 answer:
aivan3 [116]2 years ago
8 0

Answer:

The probability that 3 lights are on after the third person exited the room is 39/128

Step-by-step explanation:

In order for 6 switches to be on at the end, we need exactly 2 people turning on a switch and the other one turning one off. There are 3 possibilities:

  • The first two persons turn the switch in and the last one turns it off
  • The first and last person turn the switch in and the middle one tunrns it off
  • The first person turns the switch off and the 2 remaining turn the switch in

Note that after turning off one switch one more switch will be available to be switched in and one less will be available to be switch off. The contrary happens when someone turns in a switch.

Lets calculate the probability for the first scenario. The probability for the first person to turn the switch in is 3/8, because there are 3 lights off. For the second person, there will be only 2 lights off, thus, the probability for him or her to turn the switch in is only 2/8, leaving only 1 light off and 7 on. The third person will have, as a consecuence, a probability of 7/8 to turn off one of the 7 switches. This gives us a probability of 3/8 * 2/8 * 7/8 = 21/256 for the first scenario.

For the second scenario we will have a probability of 3/8 for the first person, a probability of 6/8 for the second one (he has to turn a switch off this time), and a probability, again, of 3/8 for the third one, giving us a probability of 3/8*6/8*3/8 = 27/256 for the second scenario.

For the third scenario, the first person has to turn off the switch, and it has a probability of 5/8 of doing so. The second person will have 4 switches to turn on, so it has a probability of 4/8 = 1/2, and the third person will have one switch less, thus, a probability of 3/8 of turning a switch on. Therefore, the probability of the third scenario is 5/8*1/2*3/8 = 15/128 = 30/256

By summing all the three disjoint scenarios, the probability that six lights are on is 21/256+27/256+30/256 = 78/256 = 39/128.

You might be interested in
How do you find the are of a circle with pi?
SCORPION-xisa [38]

Answer:

Formula: pi*r^2

Step-by-step explanation:

8 0
3 years ago
Given g(x) =3x-3 solve for x when g(x) = 6
Scilla [17]

Answer:

x=2g+1

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
Please help brainliest if correct only answer if you know
polet [3.4K]

Answer:

Ar, ar, ar, ar, ar

Step-by-step explanation:

A for Asylum (k_ll me pls)

B for Banana slit milkshake

E for Eleven years of my life wasted :')

3 0
3 years ago
Read 2 more answers
Pls help. I am not very smart!
Yanka [14]

Answer:

Umm I'm not entirely sure but I think its the last one

8 0
2 years ago
Read 2 more answers
Here are two closed containers and four balls just fit into each container. Each ball has a diameter of 60mm. Which container ha
Fittoniya [83]

Answer:

"A is smaller"

Step-by-step explanation:

The full question is attached.

<u>Surface area of cylinder:</u>

The formula is  SA=2\pi r^2 + 2\pi r h

where r is the radius and h is the height

Here, radius would be 30 since balls have diameter 60 and radius is half of that.

Also height is the diameter of 4 balls line-by-line, so height is 60*4 = 240

Now, plugging into the formula, we get:

SA=2\pi r^2 + 2\pi r h\\SA=2\pi (30)^2 + 2\pi (30) (240)\\SA=50,868

<u>Surface Area of rectangular prism:</u>

The surface area of rectangular prism is the area of all the rectangular surfaces (6 of them).

Area of top and bottom = (60+60)*(60+60) * 2 = 120*120 * 2 = 28,800

Area of 2 sides = 2 * (60*120) = 14,400

Area of front and back = 2 * (60*120) = 14,400

Total Surface Area = 28,800 + 14,400 + 14,400 = 57,600

Thus, cylinder has smaller surface area.

"A is smaller"

7 0
3 years ago
Read 2 more answers
Other questions:
  • Find the new price for the markup given. Round to the nearest cent if necessary.
    8·1 answer
  • A rectangle has a length of 16 feet and a width of 12 feet. Find the area of the rectangle in square feet.
    11·1 answer
  • Is b=1/2 a solution of the equation -4b+5 =3
    9·1 answer
  • What is 3 2/5 minus 1 9/10
    14·2 answers
  • Which rule describes the pattern below?
    14·2 answers
  • A bank has 23 employees. 3 employees get paid $20.93 an hour. 7 employees get paid $19.68 per hour. The other 13 get paid $23.00
    12·1 answer
  • Picture below! <br> What is the equation of the line in slope-intercept form?<br> y = __x +__
    5·1 answer
  • When is it appropriate to use a pie chart?
    7·1 answer
  • Find the absolute value of |-3+8i|​
    8·2 answers
  • A football stadium sells three different brands of bottled water: Crystal Clear, Pure Refresh, and Spring Fresh.
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!